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Zusammen mit dem Kathetensatz und dem Satz des Pythagoras bildet er die ",[567,1012,1013],{},"Satzgruppe des Pythagoras",[558,1015,1017],{"id":1016},"herleitung","Herleitung",[563,1019,1020,1021,719,1201,1364,1365,1619],{},"Die Höhe teilt das Dreieck in zwei kleinere rechtwinklige Dreiecke. 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p^2",[572,1062,1064,1120,1165],{"className":1063,"ariaHidden":602},[601],[572,1065,1067,1071,1111,1114,1117],{"className":1066},[606],[572,1068],{"className":1069,"style":1070},[610],"height:0.8141em;",[572,1072,1074,1077],{"className":1073},[615],[572,1075,877],{"className":1076},[615,616],[572,1078,1081],{"className":1079},[1080],"msupsub",[572,1082,1085],{"className":1083},[1084],"vlist-t",[572,1086,1089],{"className":1087},[1088],"vlist-r",[572,1090,1093],{"className":1091,"style":1070},[1092],"vlist",[572,1094,1096,1101],{"style":1095},"top:-3.063em;margin-right:0.05em;",[572,1097],{"className":1098,"style":1100},[1099],"pstrut","height:2.7em;",[572,1102,1108],{"className":1103},[1104,1105,1106,1107],"sizing","reset-size6","size3","mtight",[572,1109,1041],{"className":1110},[615,1107],[572,1112],{"className":1113,"style":816},[795],[572,1115,773],{"className":1116},[820],[572,1118],{"className":1119,"style":816},[795],[572,1121,1123,1127,1156,1159,1162],{"className":1122},[606],[572,1124],{"className":1125,"style":1126},[610],"height:0.8974em;vertical-align:-0.0833em;",[572,1128,1130,1133],{"className":1129},[615],[572,1131,671],{"className":1132},[615,616],[572,1134,1136],{"className":1135},[1080],[572,1137,1139],{"className":1138},[1084],[572,1140,1142],{"className":1141},[1088],[572,1143,1145],{"className":1144,"style":1070},[1092],[572,1146,1147,1150],{"style":1095},[572,1148],{"className":1149,"style":1100},[1099],[572,1151,1153],{"className":1152},[1104,1105,1106,1107],[572,1154,1041],{"className":1155},[615,1107],[572,1157],{"className":1158,"style":796},[795],[572,1160,768],{"className":1161},[800],[572,1163],{"className":1164,"style":796},[795],[572,1166,1168,1172],{"className":1167},[606],[572,1169],{"className":1170,"style":1171},[610],"height:1.0085em;vertical-align:-0.1944em;",[572,1173,1175,1178],{"className":1174},[615],[572,1176,563],{"className":1177},[615,616],[572,1179,1181],{"className":1180},[1080],[572,1182,1184],{"className":1183},[1084],[572,1185,1187],{"className":1186},[1088],[572,1188,1190],{"className":1189,"style":1070},[1092],[572,1191,1192,1195],{"style":1095},[572,1193],{"className":1194,"style":1100},[1099],[572,1196,1198],{"className":1197},[1104,1105,1106,1107],[572,1199,1041],{"className":1200},[615,1107],[572,1202,1204,1238],{"className":1203},[575],[572,1205,1207],{"className":1206},[579],[581,1208,1209],{"xmlns":583},[585,1210,1211,1235],{},[588,1212,1213,1219,1221,1227,1229],{},[1034,1214,1215,1217],{},[591,1216,936],{},[1039,1218,1041],{},[766,1220,773],{},[1034,1222,1223,1225],{},[591,1224,671],{},[1039,1226,1041],{},[766,1228,768],{},[1034,1230,1231,1233],{},[591,1232,734],{},[1039,1234,1041],{},[595,1236,1237],{"encoding":597},"b^2 = h^2 + q^2",[572,1239,1241,1285,1329],{"className":1240,"ariaHidden":602},[601],[572,1242,1244,1247,1276,1279,1282],{"className":1243},[606],[572,1245],{"className":1246,"style":1070},[610],[572,1248,1250,1253],{"className":1249},[615],[572,1251,936],{"className":1252},[615,616],[572,1254,1256],{"className":1255},[1080],[572,1257,1259],{"className":1258},[1084],[572,1260,1262],{"className":1261},[1088],[572,1263,1265],{"className":1264,"style":1070},[1092],[572,1266,1267,1270],{"style":1095},[572,1268],{"className":1269,"style":1100},[1099],[572,1271,1273],{"className":1272},[1104,1105,1106,1107],[572,1274,1041],{"className":1275},[615,1107],[572,1277],{"className":1278,"style":816},[795],[572,1280,773],{"className":1281},[820],[572,1283],{"className":1284,"style":816},[795],[572,1286,1288,1291,1320,1323,1326],{"className":1287},[606],[572,1289],{"className":1290,"style":1126},[610],[572,1292,1294,1297],{"className":1293},[615],[572,1295,671],{"className":1296},[615,616],[572,1298,1300],{"className":1299},[1080],[572,1301,1303],{"className":1302},[1084],[572,1304,1306],{"className":1305},[1088],[572,1307,1309],{"className":1308,"style":1070},[1092],[572,1310,1311,1314],{"style":1095},[572,1312],{"className":1313,"style":1100},[1099],[572,1315,1317],{"className":1316},[1104,1105,1106,1107],[572,1318,1041],{"className":1319},[615,1107],[572,1321],{"className":1322,"style":796},[795],[572,1324,768],{"className":1325},[800],[572,1327],{"className":1328,"style":796},[795],[572,1330,1332,1335],{"className":1331},[606],[572,1333],{"className":1334,"style":1171},[610],[572,1336,1338,1341],{"className":1337},[615],[572,1339,734],{"className":1340,"style":749},[615,616],[572,1342,1344],{"className":1343},[1080],[572,1345,1347],{"className":1346},[1084],[572,1348,1350],{"className":1349},[1088],[572,1351,1353],{"className":1352,"style":1070},[1092],[572,1354,1355,1358],{"style":1095},[572,1356],{"className":1357,"style":1100},[1099],[572,1359,1361],{"className":1360},[1104,1105,1106,1107],[572,1362,1041],{"className":1363},[615,1107],". Im großen Dreieck gilt ",[572,1366,1368,1421],{"className":1367},[575],[572,1369,1371],{"className":1370},[579],[581,1372,1373],{"xmlns":583},[585,1374,1375,1418],{},[588,1376,1377,1383,1385,1391,1393,1399,1401,1405,1407,1409,1411],{},[1034,1378,1379,1381],{},[591,1380,877],{},[1039,1382,1041],{},[766,1384,768],{},[1034,1386,1387,1389],{},[591,1388,936],{},[1039,1390,1041],{},[766,1392,773],{},[1034,1394,1395,1397],{},[591,1396,633],{},[1039,1398,1041],{},[766,1400,773],{},[766,1402,1404],{"stretchy":1403},"false","(",[591,1406,563],{},[766,1408,768],{},[591,1410,734],{},[1034,1412,1413,1416],{},[766,1414,1415],{"stretchy":1403},")",[1039,1417,1041],{},[595,1419,1420],{"encoding":597},"a^2 + b^2 = c^2 = (p + q)^2",[572,1422,1424,1468,1512,1556,1579],{"className":1423,"ariaHidden":602},[601],[572,1425,1427,1430,1459,1462,1465],{"className":1426},[606],[572,1428],{"className":1429,"style":1126},[610],[572,1431,1433,1436],{"className":1432},[615],[572,1434,877],{"className":1435},[615,616],[572,1437,1439],{"className":1438},[1080],[572,1440,1442],{"className":1441},[1084],[572,1443,1445],{"className":1444},[1088],[572,1446,1448],{"className":1447,"style":1070},[1092],[572,1449,1450,1453],{"style":1095},[572,1451],{"className":1452,"style":1100},[1099],[572,1454,1456],{"className":1455},[1104,1105,1106,1107],[572,1457,1041],{"className":1458},[615,1107],[572,1460],{"className":1461,"style":796},[795],[572,1463,768],{"className":1464},[800],[572,1466],{"className":1467,"style":796},[795],[572,1469,1471,1474,1503,1506,1509],{"className":1470},[606],[572,1472],{"className":1473,"style":1070},[610],[572,1475,1477,1480],{"className":1476},[615],[572,1478,936],{"className":1479},[615,616],[572,1481,1483],{"className":1482},[1080],[572,1484,1486],{"className":1485},[1084],[572,1487,1489],{"className":1488},[1088],[572,1490,1492],{"className":1491,"style":1070},[1092],[572,1493,1494,1497],{"style":1095},[572,1495],{"className":1496,"style":1100},[1099],[572,1498,1500],{"className":1499},[1104,1105,1106,1107],[572,1501,1041],{"className":1502},[615,1107],[572,1504],{"className":1505,"style":816},[795],[572,1507,773],{"className":1508},[820],[572,1510],{"className":1511,"style":816},[795],[572,1513,1515,1518,1547,1550,1553],{"className":1514},[606],[572,1516],{"className":1517,"style":1070},[610],[572,1519,1521,1524],{"className":1520},[615],[572,1522,633],{"className":1523},[615,616],[572,1525,1527],{"className":1526},[1080],[572,1528,1530],{"className":1529},[1084],[572,1531,1533],{"className":1532},[1088],[572,1534,1536],{"className":1535,"style":1070},[1092],[572,1537,1538,1541],{"style":1095},[572,1539],{"className":1540,"style":1100},[1099],[572,1542,1544],{"className":1543},[1104,1105,1106,1107],[572,1545,1041],{"className":1546},[615,1107],[572,1548],{"className":1549,"style":816},[795],[572,1551,773],{"className":1552},[820],[572,1554],{"className":1555,"style":816},[795],[572,1557,1559,1563,1567,1570,1573,1576],{"className":1558},[606],[572,1560],{"className":1561,"style":1562},[610],"height:1em;vertical-align:-0.25em;",[572,1564,1404],{"className":1565},[1566],"mopen",[572,1568,563],{"className":1569},[615,616],[572,1571],{"className":1572,"style":796},[795],[572,1574,768],{"className":1575},[800],[572,1577],{"className":1578,"style":796},[795],[572,1580,1582,1586,1589],{"className":1581},[606],[572,1583],{"className":1584,"style":1585},[610],"height:1.0641em;vertical-align:-0.25em;",[572,1587,734],{"className":1588,"style":749},[615,616],[572,1590,1593,1596],{"className":1591},[1592],"mclose",[572,1594,1415],{"className":1595},[1592],[572,1597,1599],{"className":1598},[1080],[572,1600,1602],{"className":1601},[1084],[572,1603,1605],{"className":1604},[1088],[572,1606,1608],{"className":1607,"style":1070},[1092],[572,1609,1610,1613],{"style":1095},[572,1611],{"className":1612,"style":1100},[1099],[572,1614,1616],{"className":1615},[1104,1105,1106,1107],[572,1617,1041],{"className":1618},[615,1107],". Einsetzen:",[572,1621,1624],{"className":1622},[1623],"katex-display",[572,1625,1627,1709],{"className":1626},[575],[572,1628,1630],{"className":1629},[579],[581,1631,1633],{"xmlns":583,"display":1632},"block",[585,1634,1635,1706],{},[588,1636,1637,1639,1645,1647,1653,1655,1661,1663,1669,1671,1673,1675,1677,1679,1685,1689,1692,1694,1700,1702,1704],{},[1039,1638,1041],{},[1034,1640,1641,1643],{},[591,1642,671],{},[1039,1644,1041],{},[766,1646,768],{},[1034,1648,1649,1651],{},[591,1650,563],{},[1039,1652,1041],{},[766,1654,768],{},[1034,1656,1657,1659],{},[591,1658,734],{},[1039,1660,1041],{},[766,1662,773],{},[1034,1664,1665,1667],{},[591,1666,563],{},[1039,1668,1041],{},[766,1670,768],{},[1039,1672,1041],{},[591,1674,563],{},[591,1676,734],{},[766,1678,768],{},[1034,1680,1681,1683],{},[591,1682,734],{},[1039,1684,1041],{},[1686,1687,1688],"mtext",{},"  ",[766,1690,1691],{},"⇒",[1686,1693,1688],{},[1034,1695,1696,1698],{},[591,1697,671],{},[1039,1699,1041],{},[766,1701,773],{},[591,1703,563],{},[591,1705,734],{},[595,1707,1708],{"encoding":597},"2h^2 + p^2 + q^2 = p^2 + 2pq + q^2\n\\;\\Rightarrow\\;\nh^2 = pq",[572,1710,1712,1762,1807,1851,1895,1918,1968,2012],{"className":1711,"ariaHidden":602},[601],[572,1713,1715,1719,1722,1753,1756,1759],{"className":1714},[606],[572,1716],{"className":1717,"style":1718},[610],"height:0.9474em;vertical-align:-0.0833em;",[572,1720,1041],{"className":1721},[615],[572,1723,1725,1728],{"className":1724},[615],[572,1726,671],{"className":1727},[615,616],[572,1729,1731],{"className":1730},[1080],[572,1732,1734],{"className":1733},[1084],[572,1735,1737],{"className":1736},[1088],[572,1738,1741],{"className":1739,"style":1740},[1092],"height:0.8641em;",[572,1742,1744,1747],{"style":1743},"top:-3.113em;margin-right:0.05em;",[572,1745],{"className":1746,"style":1100},[1099],[572,1748,1750],{"className":1749},[1104,1105,1106,1107],[572,1751,1041],{"className":1752},[615,1107],[572,1754],{"className":1755,"style":796},[795],[572,1757,768],{"className":1758},[800],[572,1760],{"className":1761,"style":796},[795],[572,1763,1765,1769,1798,1801,1804],{"className":1764},[606],[572,1766],{"className":1767,"style":1768},[610],"height:1.0585em;vertical-align:-0.1944em;",[572,1770,1772,1775],{"className":1771},[615],[572,1773,563],{"className":1774},[615,616],[572,1776,1778],{"className":1777},[1080],[572,1779,1781],{"className":1780},[1084],[572,1782,1784],{"className":1783},[1088],[572,1785,1787],{"className":1786,"style":1740},[1092],[572,1788,1789,1792],{"style":1743},[572,1790],{"className":1791,"style":1100},[1099],[572,1793,1795],{"className":1794},[1104,1105,1106,1107],[572,1796,1041],{"className":1797},[615,1107],[572,1799],{"className":1800,"style":796},[795],[572,1802,768],{"className":1803},[800],[572,1805],{"className":1806,"style":796},[795],[572,1808,1810,1813,1842,1845,1848],{"className":1809},[606],[572,1811],{"className":1812,"style":1768},[610],[572,1814,1816,1819],{"className":1815},[615],[572,1817,734],{"className":1818,"style":749},[615,616],[572,1820,1822],{"className":1821},[1080],[572,1823,1825],{"className":1824},[1084],[572,1826,1828],{"className":1827},[1088],[572,1829,1831],{"className":1830,"style":1740},[1092],[572,1832,1833,1836],{"style":1743},[572,1834],{"className":1835,"style":1100},[1099],[572,1837,1839],{"className":1838},[1104,1105,1106,1107],[572,1840,1041],{"className":1841},[615,1107],[572,1843],{"className":1844,"style":816},[795],[572,1846,773],{"className":1847},[820],[572,1849],{"className":1850,"style":816},[795],[572,1852,1854,1857,1886,1889,1892],{"className":1853},[606],[572,1855],{"className":1856,"style":1768},[610],[572,1858,1860,1863],{"className":1859},[615],[572,1861,563],{"className":1862},[615,616],[572,1864,1866],{"className":1865},[1080],[572,1867,1869],{"className":1868},[1084],[572,1870,1872],{"className":1871},[1088],[572,1873,1875],{"className":1874,"style":1740},[1092],[572,1876,1877,1880],{"style":1743},[572,1878],{"className":1879,"style":1100},[1099],[572,1881,1883],{"className":1882},[1104,1105,1106,1107],[572,1884,1041],{"className":1885},[615,1107],[572,1887],{"className":1888,"style":796},[795],[572,1890,768],{"className":1891},[800],[572,1893],{"className":1894,"style":796},[795],[572,1896,1898,1902,1905,1909,1912,1915],{"className":1897},[606],[572,1899],{"className":1900,"style":1901},[610],"height:0.8389em;vertical-align:-0.1944em;",[572,1903,1041],{"className":1904},[615],[572,1906,1908],{"className":1907,"style":749},[615,616],"pq",[572,1910],{"className":1911,"style":796},[795],[572,1913,768],{"className":1914},[800],[572,1916],{"className":1917,"style":796},[795],[572,1919,1921,1924,1953,1956,1959,1962,1965],{"className":1920},[606],[572,1922],{"className":1923,"style":1768},[610],[572,1925,1927,1930],{"className":1926},[615],[572,1928,734],{"className":1929,"style":749},[615,616],[572,1931,1933],{"className":1932},[1080],[572,1934,1936],{"className":1935},[1084],[572,1937,1939],{"className":1938},[1088],[572,1940,1942],{"className":1941,"style":1740},[1092],[572,1943,1944,1947],{"style":1743},[572,1945],{"className":1946,"style":1100},[1099],[572,1948,1950],{"className":1949},[1104,1105,1106,1107],[572,1951,1041],{"className":1952},[615,1107],[572,1954],{"className":1955,"style":816},[795],[572,1957],{"className":1958,"style":816},[795],[572,1960,1691],{"className":1961},[820],[572,1963],{"className":1964,"style":816},[795],[572,1966],{"className":1967,"style":816},[795],[572,1969,1971,1974,2003,2006,2009],{"className":1970},[606],[572,1972],{"className":1973,"style":1740},[610],[572,1975,1977,1980],{"className":1976},[615],[572,1978,671],{"className":1979},[615,616],[572,1981,1983],{"className":1982},[1080],[572,1984,1986],{"className":1985},[1084],[572,1987,1989],{"className":1988},[1088],[572,1990,1992],{"className":1991,"style":1740},[1092],[572,1993,1994,1997],{"style":1743},[572,1995],{"className":1996,"style":1100},[1099],[572,1998,2000],{"className":1999},[1104,1105,1106,1107],[572,2001,1041],{"className":2002},[615,1107],[572,2004],{"className":2005,"style":816},[795],[572,2007,773],{"className":2008},[820],[572,2010],{"className":2011,"style":816},[795],[572,2013,2015,2018],{"className":2014},[606],[572,2016],{"className":2017,"style":715},[610],[572,2019,1908],{"className":2020,"style":749},[615,616],[558,2022,2024],{"id":2023},"beispiele","Beispiele",[563,2026,2027,2028,2098,2099,2164,2165,2230,2231,2309,2310,2338,2339,2309,2413,2441,2442,2484],{},"Im rechtwinkligen Dreieck mit den Katheten ",[572,2029,2031,2056],{"className":2030},[575],[572,2032,2034],{"className":2033},[579],[581,2035,2036],{"xmlns":583},[585,2037,2038,2053],{},[588,2039,2040,2042,2044,2047,2050],{},[591,2041,877],{},[766,2043,773],{},[1039,2045,2046],{},"3",[1686,2048,2049],{}," ",[1686,2051,2052],{},"cm",[595,2054,2055],{"encoding":597},"a = 3\\,\\text{cm}",[572,2057,2059,2077],{"className":2058,"ariaHidden":602},[601],[572,2060,2062,2065,2068,2071,2074],{"className":2061},[606],[572,2063],{"className":2064,"style":645},[610],[572,2066,877],{"className":2067},[615,616],[572,2069],{"className":2070,"style":816},[795],[572,2072,773],{"className":2073},[820],[572,2075],{"className":2076,"style":816},[795],[572,2078,2080,2084,2087,2091],{"className":2079},[606],[572,2081],{"className":2082,"style":2083},[610],"height:0.6444em;",[572,2085,2046],{"className":2086},[615],[572,2088],{"className":2089,"style":2090},[795],"margin-right:0.1667em;",[572,2092,2095],{"className":2093},[615,2094],"text",[572,2096,2052],{"className":2097},[615],", ",[572,2100,2102,2125],{"className":2101},[575],[572,2103,2105],{"className":2104},[579],[581,2106,2107],{"xmlns":583},[585,2108,2109,2122],{},[588,2110,2111,2113,2115,2118,2120],{},[591,2112,936],{},[766,2114,773],{},[1039,2116,2117],{},"4",[1686,2119,2049],{},[1686,2121,2052],{},[595,2123,2124],{"encoding":597},"b = 4\\,\\text{cm}",[572,2126,2128,2146],{"className":2127,"ariaHidden":602},[601],[572,2129,2131,2134,2137,2140,2143],{"className":2130},[606],[572,2132],{"className":2133,"style":683},[610],[572,2135,936],{"className":2136},[615,616],[572,2138],{"className":2139,"style":816},[795],[572,2141,773],{"className":2142},[820],[572,2144],{"className":2145,"style":816},[795],[572,2147,2149,2152,2155,2158],{"className":2148},[606],[572,2150],{"className":2151,"style":2083},[610],[572,2153,2117],{"className":2154},[615],[572,2156],{"className":2157,"style":2090},[795],[572,2159,2161],{"className":2160},[615,2094],[572,2162,2052],{"className":2163},[615]," und der Hypotenuse ",[572,2166,2168,2191],{"className":2167},[575],[572,2169,2171],{"className":2170},[579],[581,2172,2173],{"xmlns":583},[585,2174,2175,2188],{},[588,2176,2177,2179,2181,2184,2186],{},[591,2178,633],{},[766,2180,773],{},[1039,2182,2183],{},"5",[1686,2185,2049],{},[1686,2187,2052],{},[595,2189,2190],{"encoding":597},"c = 5\\,\\text{cm}",[572,2192,2194,2212],{"className":2193,"ariaHidden":602},[601],[572,2195,2197,2200,2203,2206,2209],{"className":2196},[606],[572,2198],{"className":2199,"style":645},[610],[572,2201,633],{"className":2202},[615,616],[572,2204],{"className":2205,"style":816},[795],[572,2207,773],{"className":2208},[820],[572,2210],{"className":2211,"style":816},[795],[572,2213,2215,2218,2221,2224],{"className":2214},[606],[572,2216],{"className":2217,"style":2083},[610],[572,2219,2183],{"className":2220},[615],[572,2222],{"className":2223,"style":2090},[795],[572,2225,2227],{"className":2226},[615,2094],[572,2228,2052],{"className":2229},[615]," sind die Hypotenusenabschnitte ",[572,2232,2234,2257],{"className":2233},[575],[572,2235,2237],{"className":2236},[579],[581,2238,2239],{"xmlns":583},[585,2240,2241,2254],{},[588,2242,2243,2245,2247,2250,2252],{},[591,2244,563],{},[766,2246,773],{},[1039,2248,2249],{},"1,8",[1686,2251,2049],{},[1686,2253,2052],{},[595,2255,2256],{"encoding":597},"p = 1{,}8\\,\\text{cm}",[572,2258,2260,2278],{"className":2259,"ariaHidden":602},[601],[572,2261,2263,2266,2269,2272,2275],{"className":2262},[606],[572,2264],{"className":2265,"style":715},[610],[572,2267,563],{"className":2268},[615,616],[572,2270],{"className":2271,"style":816},[795],[572,2273,773],{"className":2274},[820],[572,2276],{"className":2277,"style":816},[795],[572,2279,2281,2284,2288,2296,2300,2303],{"className":2280},[606],[572,2282],{"className":2283,"style":1901},[610],[572,2285,2287],{"className":2286},[615],"1",[572,2289,2291],{"className":2290},[615],[572,2292,2295],{"className":2293},[2294],"mpunct",",",[572,2297,2299],{"className":2298},[615],"8",[572,2301],{"className":2302,"style":2090},[795],[572,2304,2306],{"className":2305},[615,2094],[572,2307,2052],{"className":2308},[615]," (an ",[572,2311,2313,2326],{"className":2312},[575],[572,2314,2316],{"className":2315},[579],[581,2317,2318],{"xmlns":583},[585,2319,2320,2324],{},[588,2321,2322],{},[591,2323,877],{},[595,2325,877],{"encoding":597},[572,2327,2329],{"className":2328,"ariaHidden":602},[601],[572,2330,2332,2335],{"className":2331},[606],[572,2333],{"className":2334,"style":645},[610],[572,2336,877],{"className":2337},[615,616],") und ",[572,2340,2342,2365],{"className":2341},[575],[572,2343,2345],{"className":2344},[579],[581,2346,2347],{"xmlns":583},[585,2348,2349,2362],{},[588,2350,2351,2353,2355,2358,2360],{},[591,2352,734],{},[766,2354,773],{},[1039,2356,2357],{},"3,2",[1686,2359,2049],{},[1686,2361,2052],{},[595,2363,2364],{"encoding":597},"q = 3{,}2\\,\\text{cm}",[572,2366,2368,2386],{"className":2367,"ariaHidden":602},[601],[572,2369,2371,2374,2377,2380,2383],{"className":2370},[606],[572,2372],{"className":2373,"style":715},[610],[572,2375,734],{"className":2376,"style":749},[615,616],[572,2378],{"className":2379,"style":816},[795],[572,2381,773],{"className":2382},[820],[572,2384],{"className":2385,"style":816},[795],[572,2387,2389,2392,2395,2401,2404,2407],{"className":2388},[606],[572,2390],{"className":2391,"style":1901},[610],[572,2393,2046],{"className":2394},[615],[572,2396,2398],{"className":2397},[615],[572,2399,2295],{"className":2400},[2294],[572,2402,1041],{"className":2403},[615],[572,2405],{"className":2406,"style":2090},[795],[572,2408,2410],{"className":2409},[615,2094],[572,2411,2052],{"className":2412},[615],[572,2414,2416,2429],{"className":2415},[575],[572,2417,2419],{"className":2418},[579],[581,2420,2421],{"xmlns":583},[585,2422,2423,2427],{},[588,2424,2425],{},[591,2426,936],{},[595,2428,936],{"encoding":597},[572,2430,2432],{"className":2431,"ariaHidden":602},[601],[572,2433,2435,2438],{"className":2434},[606],[572,2436],{"className":2437,"style":683},[610],[572,2439,936],{"className":2440},[615,616],"), zusammen ",[572,2443,2445,2463],{"className":2444},[575],[572,2446,2448],{"className":2447},[579],[581,2449,2450],{"xmlns":583},[585,2451,2452,2460],{},[588,2453,2454,2456,2458],{},[1039,2455,2183],{},[1686,2457,2049],{},[1686,2459,2052],{},[595,2461,2462],{"encoding":597},"5\\,\\text{cm}",[572,2464,2466],{"className":2465,"ariaHidden":602},[601],[572,2467,2469,2472,2475,2478],{"className":2468},[606],[572,2470],{"className":2471,"style":2083},[610],[572,2473,2183],{"className":2474},[615],[572,2476],{"className":2477,"style":2090},[795],[572,2479,2481],{"className":2480},[615,2094],[572,2482,2052],{"className":2483},[615],":",[572,2486,2488],{"className":2487},[1623],[572,2489,2491,2568],{"className":2490},[575],[572,2492,2494],{"className":2493},[579],[581,2495,2496],{"xmlns":583,"display":1632},[585,2497,2498,2565],{},[588,2499,2500,2506,2508,2510,2512,2514,2517,2519,2521,2523,2525,2528,2530,2536,2539,2541,2543,2545,2547,2552,2554,2556,2558,2561,2563],{},[1034,2501,2502,2504],{},[591,2503,671],{},[1039,2505,1041],{},[766,2507,773],{},[1039,2509,2249],{},[1686,2511,2049],{},[1686,2513,2052],{},[766,2515,2516],{},"⋅",[1039,2518,2357],{},[1686,2520,2049],{},[1686,2522,2052],{},[766,2524,773],{},[1039,2526,2527],{},"5,76",[1686,2529,2049],{},[1034,2531,2532,2534],{},[1686,2533,2052],{},[1039,2535,1041],{},[795,2537],{"width":2538},"1em",[766,2540,1691],{},[795,2542],{"width":2538},[591,2544,671],{},[766,2546,773],{},[2548,2549,2550],"msqrt",{},[1039,2551,2527],{},[1686,2553,2049],{},[1686,2555,2052],{},[766,2557,773],{},[1039,2559,2560],{},"2,4",[1686,2562,2049],{},[1686,2564,2052],{},[595,2566,2567],{"encoding":597},"h^2 = 1{,}8\\,\\text{cm} \\cdot 3{,}2\\,\\text{cm} = 5{,}76\\,\\text{cm}^2\n\\quad\\Rightarrow\\quad\nh = \\sqrt{5{,}76}\\,\\text{cm} = 2{,}4\\,\\text{cm}",[572,2569,2571,2615,2651,2687,2757,2775,2877],{"className":2570,"ariaHidden":602},[601],[572,2572,2574,2577,2606,2609,2612],{"className":2573},[606],[572,2575],{"className":2576,"style":1740},[610],[572,2578,2580,2583],{"className":2579},[615],[572,2581,671],{"className":2582},[615,616],[572,2584,2586],{"className":2585},[1080],[572,2587,2589],{"className":2588},[1084],[572,2590,2592],{"className":2591},[1088],[572,2593,2595],{"className":2594,"style":1740},[1092],[572,2596,2597,2600],{"style":1743},[572,2598],{"className":2599,"style":1100},[1099],[572,2601,2603],{"className":2602},[1104,1105,1106,1107],[572,2604,1041],{"className":2605},[615,1107],[572,2607],{"className":2608,"style":816},[795],[572,2610,773],{"className":2611},[820],[572,2613],{"className":2614,"style":816},[795],[572,2616,2618,2621,2624,2630,2633,2636,2642,2645,2648],{"className":2617},[606],[572,2619],{"className":2620,"style":1901},[610],[572,2622,2287],{"className":2623},[615],[572,2625,2627],{"className":2626},[615],[572,2628,2295],{"className":2629},[2294],[572,2631,2299],{"className":2632},[615],[572,2634],{"className":2635,"style":2090},[795],[572,2637,2639],{"className":2638},[615,2094],[572,2640,2052],{"className":2641},[615],[572,2643],{"className":2644,"style":796},[795],[572,2646,2516],{"className":2647},[800],[572,2649],{"className":2650,"style":796},[795],[572,2652,2654,2657,2660,2666,2669,2672,2678,2681,2684],{"className":2653},[606],[572,2655],{"className":2656,"style":1901},[610],[572,2658,2046],{"className":2659},[615],[572,2661,2663],{"className":2662},[615],[572,2664,2295],{"className":2665},[2294],[572,2667,1041],{"className":2668},[615],[572,2670],{"className":2671,"style":2090},[795],[572,2673,2675],{"className":2674},[615,2094],[572,2676,2052],{"className":2677},[615],[572,2679],{"className":2680,"style":816},[795],[572,2682,773],{"className":2683},[820],[572,2685],{"className":2686,"style":816},[795],[572,2688,2690,2693,2696,2702,2706,2709,2741,2745,2748,2751,2754],{"className":2689},[606],[572,2691],{"className":2692,"style":1768},[610],[572,2694,2183],{"className":2695},[615],[572,2697,2699],{"className":2698},[615],[572,2700,2295],{"className":2701},[2294],[572,2703,2705],{"className":2704},[615],"76",[572,2707],{"className":2708,"style":2090},[795],[572,2710,2712,2718],{"className":2711},[615],[572,2713,2715],{"className":2714},[615,2094],[572,2716,2052],{"className":2717},[615],[572,2719,2721],{"className":2720},[1080],[572,2722,2724],{"className":2723},[1084],[572,2725,2727],{"className":2726},[1088],[572,2728,2730],{"className":2729,"style":1740},[1092],[572,2731,2732,2735],{"style":1743},[572,2733],{"className":2734,"style":1100},[1099],[572,2736,2738],{"className":2737},[1104,1105,1106,1107],[572,2739,1041],{"className":2740},[615,1107],[572,2742],{"className":2743,"style":2744},[795],"margin-right:1em;",[572,2746],{"className":2747,"style":816},[795],[572,2749,1691],{"className":2750},[820],[572,2752],{"className":2753,"style":2744},[795],[572,2755],{"className":2756,"style":816},[795],[572,2758,2760,2763,2766,2769,2772],{"className":2759},[606],[572,2761],{"className":2762,"style":683},[610],[572,2764,671],{"className":2765},[615,616],[572,2767],{"className":2768,"style":816},[795],[572,2770,773],{"className":2771},[820],[572,2773],{"className":2774,"style":816},[795],[572,2776,2778,2782,2859,2862,2868,2871,2874],{"className":2777},[606],[572,2779],{"className":2780,"style":2781},[610],"height:1.24em;vertical-align:-0.2811em;",[572,2783,2786],{"className":2784},[615,2785],"sqrt",[572,2787,2790,2850],{"className":2788},[1084,2789],"vlist-t2",[572,2791,2793,2845],{"className":2792},[1088],[572,2794,2797,2822],{"className":2795,"style":2796},[1092],"height:0.9589em;",[572,2798,2802,2806],{"className":2799,"style":2801},[2800],"svg-align","top:-3.2em;",[572,2803],{"className":2804,"style":2805},[1099],"height:3.2em;",[572,2807,2810,2813,2819],{"className":2808,"style":2809},[615],"padding-left:1em;",[572,2811,2183],{"className":2812},[615],[572,2814,2816],{"className":2815},[615],[572,2817,2295],{"className":2818},[2294],[572,2820,2705],{"className":2821},[615],[572,2823,2825,2828],{"style":2824},"top:-2.9189em;",[572,2826],{"className":2827,"style":2805},[1099],[572,2829,2833],{"className":2830,"style":2832},[2831],"hide-tail","min-width:1.02em;height:1.28em;",[2834,2835,2841],"svg",{"xmlns":2836,"width":2837,"height":2838,"viewBox":2839,"preserveAspectRatio":2840},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.28em","0 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4\\,\\text{cm}",[572,2933,2935,2953],{"className":2934,"ariaHidden":602},[601],[572,2936,2938,2941,2944,2947,2950],{"className":2937},[606],[572,2939],{"className":2940,"style":715},[610],[572,2942,563],{"className":2943},[615,616],[572,2945],{"className":2946,"style":816},[795],[572,2948,773],{"className":2949},[820],[572,2951],{"className":2952,"style":816},[795],[572,2954,2956,2959,2962,2965],{"className":2955},[606],[572,2957],{"className":2958,"style":2083},[610],[572,2960,2117],{"className":2961},[615],[572,2963],{"className":2964,"style":2090},[795],[572,2966,2968],{"className":2967},[615,2094],[572,2969,2052],{"className":2970},[615],[572,2972,2974,2997],{"className":2973},[575],[572,2975,2977],{"className":2976},[579],[581,2978,2979],{"xmlns":583},[585,2980,2981,2994],{},[588,2982,2983,2985,2987,2990,2992],{},[591,2984,734],{},[766,2986,773],{},[1039,2988,2989],{},"9",[1686,2991,2049],{},[1686,2993,2052],{},[595,2995,2996],{"encoding":597},"q = 9\\,\\text{cm}",[572,2998,3000,3018],{"className":2999,"ariaHidden":602},[601],[572,3001,3003,3006,3009,3012,3015],{"className":3002},[606],[572,3004],{"className":3005,"style":715},[610],[572,3007,734],{"className":3008,"style":749},[615,616],[572,3010],{"className":3011,"style":816},[795],[572,3013,773],{"className":3014},[820],[572,3016],{"className":3017,"style":816},[795],[572,3019,3021,3024,3027,3030],{"className":3020},[606],[572,3022],{"className":3023,"style":2083},[610],[572,3025,2989],{"className":3026},[615],[572,3028],{"className":3029,"style":2090},[795],[572,3031,3033],{"className":3032},[615,2094],[572,3034,2052],{"className":3035},[615],[572,3037,3039],{"className":3038},[1623],[572,3040,3042,3092],{"className":3041},[575],[572,3043,3045],{"className":3044},[579],[581,3046,3047],{"xmlns":583,"display":1632},[585,3048,3049,3089],{},[588,3050,3051,3053,3055,3065,3067,3069,3071,3076,3078,3080,3082,3085,3087],{},[591,3052,671],{},[766,3054,773],{},[2548,3056,3057],{},[588,3058,3059,3061,3063],{},[1039,3060,2117],{},[766,3062,2516],{},[1039,3064,2989],{},[1686,3066,2049],{},[1686,3068,2052],{},[766,3070,773],{},[2548,3072,3073],{},[1039,3074,3075],{},"36",[1686,3077,2049],{},[1686,3079,2052],{},[766,3081,773],{},[1039,3083,3084],{},"6",[1686,3086,2049],{},[1686,3088,2052],{},[595,3090,3091],{"encoding":597},"h = \\sqrt{4 \\cdot 9}\\,\\text{cm} = \\sqrt{36}\\,\\text{cm} = 6\\,\\text{cm}",[572,3093,3095,3113,3207,3278],{"className":3094,"ariaHidden":602},[601],[572,3096,3098,3101,3104,3107,3110],{"className":3097},[606],[572,3099],{"className":3100,"style":683},[610],[572,3102,671],{"className":3103},[615,616],[572,3105],{"className":3106,"style":816},[795],[572,3108,773],{"className":3109},[820],[572,3111],{"className":3112,"style":816},[795],[572,3114,3116,3120,3189,3192,3198,3201,3204],{"className":3115},[606],[572,3117],{"className":3118,"style":3119},[610],"height:1.04em;vertical-align:-0.0839em;",[572,3121,3123],{"className":3122},[615,2785],[572,3124,3126,3180],{"className":3125},[1084,2789],[572,3127,3129,3177],{"className":3128},[1088],[572,3130,3133,3160],{"className":3131,"style":3132},[1092],"height:0.9561em;",[572,3134,3137,3141],{"className":3135,"style":3136},[2800],"top:-3em;",[572,3138],{"className":3139,"style":3140},[1099],"height:3em;",[572,3142,3145,3148,3151,3154,3157],{"className":3143,"style":3144},[615],"padding-left:0.833em;",[572,3146,2117],{"className":3147},[615],[572,3149],{"className":3150,"style":796},[795],[572,3152,2516],{"className":3153},[800],[572,3155],{"className":3156,"style":796},[795],[572,3158,2989],{"className":3159},[615],[572,3161,3163,3166],{"style":3162},"top:-2.9161em;",[572,3164],{"className":3165,"style":3140},[1099],[572,3167,3170],{"className":3168,"style":3169},[2831],"min-width:0.853em;height:1.08em;",[2834,3171,3174],{"xmlns":2836,"width":2837,"height":3172,"viewBox":3173,"preserveAspectRatio":2840},"1.08em","0 0 400000 1080",[2842,3175],{"d":3176},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[572,3178,2849],{"className":3179},[2848],[572,3181,3183],{"className":3182},[1088],[572,3184,3187],{"className":3185,"style":3186},[1092],"height:0.0839em;",[572,3188],{},[572,3190],{"className":3191,"style":2090},[795],[572,3193,3195],{"className":3194},[615,2094],[572,3196,2052],{"className":3197},[615],[572,3199],{"className":3200,"style":816},[795],[572,3202,773],{"className":3203},[820],[572,3205],{"className":3206,"style":816},[795],[572,3208,3210,3213,3260,3263,3269,3272,3275],{"className":3209},[606],[572,3211],{"className":3212,"style":3119},[610],[572,3214,3216],{"className":3215},[615,2785],[572,3217,3219,3252],{"className":3218},[1084,2789],[572,3220,3222,3249],{"className":3221},[1088],[572,3223,3225,3237],{"className":3224,"style":3132},[1092],[572,3226,3228,3231],{"className":3227,"style":3136},[2800],[572,3229],{"className":3230,"style":3140},[1099],[572,3232,3234],{"className":3233,"style":3144},[615],[572,3235,3075],{"className":3236},[615],[572,3238,3239,3242],{"style":3162},[572,3240],{"className":3241,"style":3140},[1099],[572,3243,3245],{"className":3244,"style":3169},[2831],[2834,3246,3247],{"xmlns":2836,"width":2837,"height":3172,"viewBox":3173,"preserveAspectRatio":2840},[2842,3248],{"d":3176},[572,3250,2849],{"className":3251},[2848],[572,3253,3255],{"className":3254},[1088],[572,3256,3258],{"className":3257,"style":3186},[1092],[572,3259],{},[572,3261],{"className":3262,"style":2090},[795],[572,3264,3266],{"className":3265},[615,2094],[572,3267,2052],{"className":3268},[615],[572,3270],{"className":3271,"style":816},[795],[572,3273,773],{"className":3274},[820],[572,3276],{"className":3277,"style":816},[795],[572,3279,3281,3284,3287,3290],{"className":3280},[606],[572,3282],{"className":3283,"style":2083},[610],[572,3285,3084],{"className":3286},[615],[572,3288],{"className":3289,"style":2090},[795],[572,3291,3293],{"className":3292},[615,2094],[572,3294,2052],{"className":3295},[615],[558,3297,3299],{"id":3298},"typische-fehler","Typische Fehler",[3301,3302,3303,3307,3310],"ul",{},[3304,3305,3306],"li",{},"Den Satz in einem Dreieck ohne rechten Winkel anwenden.",[3304,3308,3309],{},"Mit einer anderen Höhe rechnen. Gemeint ist nur die Höhe auf die Hypotenuse, also vom rechten Winkel aus.",[3304,3311,3312,3313,3394,3395,649],{},"Am Ende die Wurzel vergessen: ",[572,3314,3316,3338],{"className":3315},[575],[572,3317,3319],{"className":3318},[579],[581,3320,3321],{"xmlns":583},[585,3322,3323,3335],{},[588,3324,3325,3331,3333],{},[1034,3326,3327,3329],{},[591,3328,671],{},[1039,3330,1041],{},[766,3332,773],{},[1039,3334,3075],{},[595,3336,3337],{"encoding":597},"h^2 = 36",[572,3339,3341,3385],{"className":3340,"ariaHidden":602},[601],[572,3342,3344,3347,3376,3379,3382],{"className":3343},[606],[572,3345],{"className":3346,"style":1070},[610],[572,3348,3350,3353],{"className":3349},[615],[572,3351,671],{"className":3352},[615,616],[572,3354,3356],{"className":3355},[1080],[572,3357,3359],{"className":3358},[1084],[572,3360,3362],{"className":3361},[1088],[572,3363,3365],{"className":3364,"style":1070},[1092],[572,3366,3367,3370],{"style":1095},[572,3368],{"className":3369,"style":1100},[1099],[572,3371,3373],{"className":3372},[1104,1105,1106,1107],[572,3374,1041],{"className":3375},[615,1107],[572,3377],{"className":3378,"style":816},[795],[572,3380,773],{"className":3381},[820],[572,3383],{"className":3384,"style":816},[795],[572,3386,3388,3391],{"className":3387},[606],[572,3389],{"className":3390,"style":2083},[610],[572,3392,3075],{"className":3393},[615]," heißt ",[572,3396,3398,3416],{"className":3397},[575],[572,3399,3401],{"className":3400},[579],[581,3402,3403],{"xmlns":583},[585,3404,3405,3413],{},[588,3406,3407,3409,3411],{},[591,3408,671],{},[766,3410,773],{},[1039,3412,3084],{},[595,3414,3415],{"encoding":597},"h = 6",[572,3417,3419,3437],{"className":3418,"ariaHidden":602},[601],[572,3420,3422,3425,3428,3431,3434],{"className":3421},[606],[572,3423],{"className":3424,"style":683},[610],[572,3426,671],{"className":3427},[615,616],[572,3429],{"className":3430,"style":816},[795],[572,3432,773],{"className":3433},[820],[572,3435],{"className":3436,"style":816},[795],[572,3438,3440,3443],{"className":3439},[606],[572,3441],{"className":3442,"style":2083},[610],[572,3444,3084],{"className":3445},[615],{"title":3447,"searchDepth":3448,"depth":3448,"links":3449},"",2,[3450,3451,3452,3453],{"id":560,"depth":3448,"text":561},{"id":1016,"depth":3448,"text":1017},{"id":2023,"depth":3448,"text":2024},{"id":3298,"depth":3448,"text":3299},[3455,3458,3461,3464,3467,3469],{"lhs":3456,"rhs":3457},"(p + q)^2","(p*q + p^2) + (p*q + q^2)",{"lhs":3459,"rhs":3460},"(a*b)^2 \u002F (a^2 + b^2)","sqrt(a^2 - (a*b)^2\u002F(a^2 + b^2)) * sqrt(b^2 - (a*b)^2\u002F(a^2 + b^2))",{"lhs":3462,"rhs":3463},"1.8 * 3.2","5.76",{"lhs":3465,"rhs":3466},"sqrt(5.76)","2.4",{"lhs":3468,"rhs":2183},"1.8 + 3.2",{"lhs":3470,"rhs":3084},"sqrt(4 * 9)","\\gamma = 90^\\circ","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>γ\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmsup>\u003Cmn>90\u003C\u002Fmn>\u003Cmo>∘\u003C\u002Fmo>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\gamma = 90^\\circ\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0556em;\">γ\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan 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class=\"fig-dot\"\u002F>\u003Cpath d=\"M 194.4 144 L 194.4 132 L 182.4 132\" class=\"fig-mark\"\u002F>\u003Ccircle cx=\"188.4\" cy=\"138\" r=\"1.5\" class=\"fig-dot\"\u002F>\u003Ctext x=\"105.6\" y=\"160.8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">q\u003C\u002Ftext>\u003Ctext x=\"225.6\" y=\"160.8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">p\u003C\u002Ftext>\u003Ctext x=\"192.96\" y=\"91.2\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">h\u003C\u002Ftext>\u003Ctext x=\"240.96\" y=\"74.88\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"94.08\" y=\"71.04\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">b\u003C\u002Ftext>\u003Ccircle cx=\"28.8\" cy=\"144\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"10.8\" y=\"148\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label 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q\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8641em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">h\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","middle",{},"\u002Fde\u002Fformulas\u002Fmath\u002Fgeometry\u002Fhoehensatz",[],[3554,3555,3556],"leg-theorem","pythagorean-theorem","triangle-area",{"title":548,"description":3447},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fhoehensatz","Im rechtwinkligen Dreieck ist das Quadrat der Höhe gleich dem Produkt der beiden Hypotenusenabschnitte.",[3561,3562,3563,3564],"rechtwinkliges dreieck","höhe","hypotenusenabschnitt","satzgruppe des pythagoras",[3566,3569,3572,3575],{"symbol":671,"meaning":3567,"symbolHtml":3568},"Höhe auf die Hypotenuse, vom rechten Winkel senkrecht auf c","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>h\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation 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style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":734,"meaning":3573,"symbolHtml":3574},"an der Kathete b anliegender Hypotenusenabschnitt","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>q\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">q\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3576,"meaning":3577,"symbolHtml":3578},"\\gamma","Winkel bei C, gegenüber der Hypotenuse c","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>γ\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\gamma\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" 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